Yet the country's police chief said detectives ruled out murder charges against Winnie Madikizela-Mandela, despite claims by one of the killers that Winnie offered 20,000 rand (4,200 dollars) to commit the crime.
Former human rights lawyer Azar Cachalia, now secretary for safety and security, testified that a statement by Winnie soon after Asvat's January 1989 murder prompted some anti-apartheid leaders to quietly suspect her.
He was addressing a hearing of the Truth and Reconciliation Commission which is probing at least 18 human rights crimes, including eight killings, linked to Madikizela-Mandela and her supporters.
One of two men convicted of Asvat's murder, Cyril Zakhele Mbatha, said in an interview with BBC television that Madikizela-Mandela gave him the gun he used in the killing.
Cachalia told the panel that at first he didn't suspect Madikizela-Mandela of the doctor's murder, because she had close ties with Asvat and his family.
But after she reportedly told a local media outlet that she knew "why Asvat was killed," Cachalia said he and other anti-apartheid leaders began to harbour suspicions.
While he did not have "direct information" about the murder, Cachalia said: "One thing that was strange to me.... she said she knew exactly why Dr. Asvat had been killed."
Those suspicions "were in the back of my mind" when anti-apartheid leaders later distanced themselves from Madikizela-Mandela.
At the time she was linked to the murder of child activist Stompie Seipei and the beatings of several others.
South African Police Services Commissioner George Fivaz said officers investigated accusations of her involvement in the doctor's murder in 1995, but "no new evidence could be found."
Prosecutors deemed the available evidence insufficient "for a successful prosecution of Mrs. Madikizela-Mandela as she ... cannot be connected with the crime," Fivaz said.
He added that Winnie's chief accuser at the time, exiled witness Katiza Cebekhulu, was unreliable and had given four separate versions to authorities.
Fivaz said he hoped the detectives handling the case, whose reliability was questioned by a truth commission official, had been "thorough" in their probe.
"If we haven't, I'll be very disappointed," the police chief said.
According to truth commission investigators, Mbatha will tell the hearing that he was offered 20,000 rand (4,200 dollars) for killing the doctor.
Mbatha said in the BBC interview he believed Winnie wanted Asvat dead because the doctor refused to provide false medical records clearing her of involvement in the death of Seipei, whom Madikizela-Mandela accused of being a police informer.
Seipei was killed by Winnie's bodyguard, Jerry Richardson, who has been jailed for life.
Richardson told journalists recently he killed Seipei on the orders of Winnie, whom he called "mama."
At the end of his testimony, Cachalia issued a personal plea to Madikizela-Mandela to admit her role in human rights abuses.
"I hope that for the sake of your inner tranquility, and for the good of the country, you take the commission into your confidence when you come forward to testify," Cachalia said looking directly at her.
"I don't know the level of responsibility you had in each of the cases," Cachalia said. "If I am proven to be wrong in any of my statements, I will tender a public apology to you."